Question: Solve for $x$ and $y$ using elimination. ${-2x+5y = 41}$ ${2x+6y = 58}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-2x$ and $2x$ cancel out. $11y = 99$ $\dfrac{11y}{{11}} = \dfrac{99}{{11}}$ ${y = 9}$ Now that you know ${y = 9}$ , plug it back into $\thinspace {-2x+5y = 41}\thinspace$ to find $x$ ${-2x + 5}{(9)}{= 41}$ $-2x+45 = 41$ $-2x+45{-45} = 41{-45}$ $-2x = -4$ $\dfrac{-2x}{{-2}} = \dfrac{-4}{{-2}}$ ${x = 2}$ You can also plug ${y = 9}$ into $\thinspace {2x+6y = 58}\thinspace$ and get the same answer for $x$ : ${2x + 6}{(9)}{= 58}$ ${x = 2}$